The factorization of the given expression is 5x(5x - 4y) - y(21y + 10z) - z².
Factorization of algebraic expression:The factorization of an algebraic expression is the process of finding two or more factors, whose multiplication results back in the given expression.
From the information given:
The factorization of 25x^2-20xy-21y^2+10yz-z^2 can be computed as:
= 5x(5x - 4y) - y(21y + 10z) - z²
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please help me I don't understand this
Answer:
A. perimeter 200
area 2356
B. Perimeter
C. Area
Step-by-step explanation:
A. Perimeter = 2(base+ height) = 2(62+38)= 200
BASE *HEIGHT (62*38)= 2356
Answer:
(a) Perimeter = 200 inches
Area 2356 inches squared
(b) Area
(c) Perimeter
Step-by-step explanation:
(a) Perimeter = [tex]2(62+38)=200[/tex] inches
Area = [tex]38\times62=2356[/tex] inches squared
(b) Area (rectangle)
(c) Perimeter (line)
Describe the steps you used to solve the equation and
find the amount of Carrie's allowance.
Linear equation:a+a+8=22
Answer:
Carrie's allowance is 7.
Step-by-step explanation:
Use the equation to find a.
a+a+8=22
First, combine like terms.
2a+8=22
Subtract 8 from both sides.
2a+8-8=22-8
2a=14
Divide 2 from both sides.
2a/2=14/2
a=7
Hope this helps!
If not, I am sorry.
Divide x ^ 4 + x - 1 by x - 1
Answer:
Graph for (x^4+x-1)/(x-1)
Step-by-step explanation:
Graph for (x^4+x-1)/(x-1)
The required, divide is given by [tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex]
Fraction of polynomial is, in the numerator and in the denominator of a fraction there is polynomial function
[tex]=x^3+\frac{x^3+x-1}{x-1}\\[/tex]
[tex]=x^3+x^2+\frac{x^2+x-1}{x-1}\\[/tex]
[tex]=x^3+x^2+x+\frac{2x-1}{x-1}\\[/tex]
[tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex]
Thus the required, divide is [tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex].
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The problem involves a conversion from feet to miles. How many feet are in one mile? Use the Internet or another resource if you need help.
The value of the 1 mile is equal to 5280 feet
We have given that,
The problem involves a conversion from feet to miles.
We have to determine how many feet are in one mile.
What is the conversion form?
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
1 mile is equal to 5280 feet
Therefore we get,
1mile=5280 feet.
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Jackie buys 5 books at $27 each and pays for them with 20 dollar bills. How many $20 bills does she need to pay for all the books?
Answer:
7
Step-by-step explanation:
5 x 27 = 135
135 ÷ 20 = 6.75
round up to 7
FIND THE AREA - GEOMETRY
The area of regular hexagon is 166.27688 inch².
What is area?The area is the amount of space within the perimeter of a 2D shape.
Given:
side = 8 inch
Using
Area of regular hexagon = 3 √3/2 * a²
= 3 √3/2 * 8*8
=96√3
= 166.27688 inch²
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Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.
Use the diagram to complete the statements.
Angles 1 and 5 are
because they are
angles.
Angles 4 and 6 are (blank)
because they are (blank)
angles.
The complete statements for the angles as in the task content are:
Angles 1 and 5 are congruent because they are corresponding angles.Angles 4 and 6 are congruent because they are alternate angles.Which statements about the angles are correct?It follows from the task content that the arrangement involves two parallel lines q and s which are cut by transversal line r.
On this note, according to the description in the task content, the angles formed at the intersections are related as follows;
Angles 1 and 5 are congruent because they are
corresponding angles.
Angles 4 and 6 are congruent because they are alternate angles.
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What is the only way to increase power of a significance test when lowering the probability of committing a Type I error
the probability of making a Type I error is equal to the significance level of power. To increase the probability of a Type I error, increase the significance level. Changing the sample size has no effect on the probability of a Type I error.
The electricity of a take a look at can be expanded in a number of methods, for example increasing the pattern length, reducing the standard errors, increasing the difference between the pattern statistic and the hypothesized parameter, or growing the alpha degree.
The chance of creating a kind I mistakes is α, that's the extent of importance you put for your hypothesis check. An α of 0.05 indicates which you are inclined to accept a five% chance which you are incorrect whilst you reject the null hypothesis. To lower this risk, you have to use a decrease cost for α
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Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
mABX = °
The length of GX is 13 and the value of ∠ABX is 22.
We know that the point at which the triangle's three interior angle bisectors converge is known as the incenter. It can be thought of as the intersection of the triangle's internal angle bisectors. Due to the junction point of the central axis being the center of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides. The center of a triangle's inscribed circle, which is the biggest circle that can fit inside the triangle, is known as the incenter.
Given that EX = 4z + 1 and XF = 2z + 7.
Since X is the incentre of this triangle ΔABC, EX = XF = GX.
Now, 4z + 1 = 2z + 7
i.e. 4z - 2z = 7 - 1
i.e. 2z = 6
i.e. z = 6/2 = 3
Then GX = 2 * 3 + 7 = 6 + 7 = 13
Also given that ∠ABC = 44°.
Since X is the incentre of this triangle ΔABC, ∠ABX = ∠CBX
Let ∠ABX = ∠CBX = y
Now y + y = 44
i.e. 2y = 44
i.e y = 44/2 = 22
Then ∠ABX = 22°
Therefore, the length of GX is 13 and the value of ∠ABX is 22°.
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Which of the following statements are true? Select all that apply.
To solve a simultaneous equation on a graph, it is important to:
Draw the graph of the two equationsFind the two lines that intersect at a common pointThis common point would then be used to find the solution of the pair of simultaneous equations.What is a Graph?This refers to the diagram that is used to show the relationship between variables that are measured along a pair of axes.
Hence, we can see that your question is incomplete so I gave you a general overview to help you get a better understanding of the given concept.
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The grocery store charges a retail price of $6.99 for a 24-pack of juice boxes. If it is wholesale, the prices are presented on the graph below. What is the difference between the retail and wholesale unit
price
The difference between the retail and wholesale unit price is $ 0.99.
What is retail price?The retail price is the price that the item is sold for to the customer.
Here,
Coordinates extracted from the graph;
(4, 1) (12, 3)
Equation of straight line (Whole sale price)
(y - y₁) = m(x - x₁)
where, m = (y₂-y₁)/(x₂-x₁)
then, m = (3-1) / (12-4)
= 2/8
= 1/4
Now, (y - 1) = 1/4 (x - 4)
4y - 4 = x - 4
x = 4y
x - 4y = 0
Now, whole sale price for 24 boxes; x = 24
24 - 4y = 0
4y = 24
y = 24/4
y = 6
The wholesale price = $ 6
The retail price = $ 6.99
The difference between retail and wholesale = Retail - Wholesale
= 6.99 - 6
= $ 0.99
Thus, the difference between the retail and wholesale unit price is $ 0.99.
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if 1€=1.50 Australian $ how many Australian $ can be made from €40?
solution:
1€=1.50
$x=€40
By using chain rule
1 × x =1.50×40
so,x=60
Hence,60 Australian $ can be exchanged from €1.5
Select the correct answer. The graph of function f is shown. An exponential function with vertex at (1, 3) and passes through (minus 2, 10), (8, 2) also intercepts the y-axis at 4 units. Function g is represented by the equation. Which statement correctly compares the two functions?
The statement which correctly compares the two functions is that: A. they have the same y-intercept and the same end behavior as x approaches ∞.
What is a function?A function is a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.
By critically observing the graph which models the function f (see attachment), we can logically deduce that the y-intercept is at four (4).
Also, from the table of function g (see attachment), we have:
At x = 0, g(x) = g(0) = 4.
In conclusion, the statement which correctly compares the two functions is that they have the same y-intercept and the same end behavior as x approaches infinity (∞).
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Complete Question:
The graph of function f is shown.
Which statement correctly compares the two functions?
A. They have the same y-intercept and the same end behavior as x approaches ∞.
B. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
C. They have the same x- and y-intercepts.
D. They have the same x-intercept and the same end behavior as x approaches ∞.
67 of the 645 parcels are damaged on the journey.
Calculate the percentage of parcels that are damaged.
Geometry help ??!!??!&&
Answer:
AB = 14
Step-by-step explanation:
We can add the segments together to find the total
AB + BC = AC
This will allow us to find x
4x+2 + 3x-1 = 22
Combine like terms
7x +1 = 22
Subtract 1 from each side
7x+1-1 = 22-1
7x = 21
Divide by 7
7x/7 = 21/7
x = 3
Now we can find the length of AB
AB = 4x+2 = 4(3)+2 = 12+2 = 14
Select the correct answer from each drop-down menu. The slope of the line in the graph is . The y-intercept is . The equation of the line is y = x .
The line with an equation of y = x have a slope of 1 and y intercept of 0.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard equation of a line is given as:
y = mx + b
Where m is the slope of the line and b is the y intercept.
The line with an equation of y = x have a slope of 1 and y intercept of 0.
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1. Try It # 1 A company sells doughnuts. They incur a fixed cost of $25,000 for rent, insurance, and other expenses. It costs $0.25 to produce each doughnut.
b. Find and interpret the y-intercept.
Answer:
The y-intercept is 25000 . The intercept is the fixed cost of the doughnut selling company.
Step-by-step explanation:
In the question, it is given that the fixed cost is $25000 and the expense to produce each doughnut is $0.25.
It is required to find and identify the y intercept.
To do so, use the equation derived in previous part of the exercise to interpret the slope. Compare the equation with standard equation of the line.
Step 1 of 1
The total cost of the company is the sum of fixed cost and the expenses for the doughnut, C=0.25x+25000.
Compare the equation with general linear equation y=mx+c.
The y-intercept is 25000 .
The intercept is the fixed cost of the doughnut selling company.
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm? Enter your answer as a decimal in the box
The measure in radians for the central angle of the circle is; 0.9 radians.
What is the angle measure in radians of the central angle?Since, the length of the arc is given as 7.2cm and it's radius is 8cm.
It follows that the angle measure of the central angle can be evaluated as follows;
7.2 = (A/6.28) × 2× 3.14 × 8
7.2 = 8A
A = 7.2/8
A = 0.9 radians.
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A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red, what is the probability that the other side is red
The probability that both sides of the card is red is 0.33
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that both sides of the card is red = total number of cards in which both sides are red / total number of cards
2/6 = 1/3 = 0.33
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Identify the center and the radius of a
circle that has a diameter with endpoints at (2, 7)
and (8, 9).
Using the mid-point concept, we have that:
The center is (5,8).The radius is of 3.16 units.What is the mid-point concept?The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.
The center of the circle is the mid-point of the coordinates of the diameter, hence:
x = (2 + 8)/2 = 5.y = (7 + 9)/2 = 8.The radius is the distance between the center and the end-points of the diameter, hence, applying the formula for the distance between two points:
[tex]r = \sqrt{(5 - 2)^2 + (8 - 7)^2} = \sqrt{10} = 3.16[/tex]
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Use AABC to find the value of cos A
(Please use photo provided)
Answer:
40/41
Step-by-step explanation:
cos = adjacent/hypotenuse
adj = 40, hyp = 41
One year, there were about 3,000 institutions of higher learning in the U.S. (including junior colleges and community colleges). As part of a continuing study of higher education, the Carnegie Commission took a simple random sample of 400 of these institutions. The average enrollment in the 400 sample schools was 3,700, and the SD was 6,500. The Commission estimates the average enrollment at all 3,000 institutions to be around 3,700; they put a give-or-take number of 325 on this estimate. There were about 600,000 faculty members at institutions of higher learning in the U.S. As part of its study, the Carnegie Commission took a simple random sample of 2,500 of these faculty persons. On the average, these 2,500 sample persons had published 1.7 research papers in the two years prior to the survey, and the SD was 2.3 papers. If possible, find an approximate 95%-confidence interval for the average number of research papers published by all 600,000 faculty members in the two years prior to the survey. If this isn't possible, explain why not.
Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.
According to the statement
Average sample =3700
SD sample =6500
Sample size =400
EV average =3700
SE average =325
Population size =3000
The boundaries of the 68% confidence interval are then 1 standard error from the estimated average:
EV average+1⋅SE average =3700+1⋅325=3700+325=4025
EV average−1⋅SE average =3700−1⋅325=3700−325=3375
Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.
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Un grupo de compañeros juegan canicas, cada uno de los 5 jugadores tiene 2 canicas y dicen que estas representan los factores de la descomposición del total de canicas. ¿Cuantas canicas tiene entre todos los jugadores en total?
Si cada jugador tiene un total de 2 canicas y hay 5 jugadores, se espera que el número total de canicas sea 10.
¿Cómo encontrar el número total de canicas?Multiplica el número de canicas por el de jugadores:
Número de canicas: 2Número de jugadores: 52 x 5 = 10 canicas.¿Cómo se puede descomponer este factor?Este factor se puede descomponer así:
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PLEASE HELP
place the figure in a coordinate plane and find the indicated length
an isosceles triangle with a base length of 60 units and a height of 50 units; find the length of one of the legs
Thanks
The length of one of the legs says line AC is 58.31.
How do we place a figure in a coordinate plane?A figure can be placed in a coordinate plane on the graph by determining the coordinate of the vertices.
For the given isosceles triangle with:
The base length of 60 units and A height of 50 units.The coordinate of the vertices are:
∠A = (0,0)∠B = (60, 0)∠C = (30, 50)The length of one leg is calculated as follows:
[tex]\mathbf{AC= \sqrt{(50-0)^2+(30-0)^2}}}[/tex]
AC = [tex]\mathbf{\sqrt{2500+900}}[/tex]
AC = [tex]\mathbf{\sqrt{3400}}[/tex]
AC = 58.31
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Total area=
Help please thanks you
Answer: 94
Step-by-step explanation:
The area of each of the top and bottom face is [tex](4)(6)-(2)(2)=20[/tex].
The area of each of the side faces is 12.
The area of each of the faces facing out is 6.
The area of each of the 3 'inner' faces is also 6.
Adding these together,
[tex]20(2)+12(2)+6(2)+6(3)=94[/tex]
I need the answers for number 9 and 10
How do you solve this?
It looks like your equations are
7M - 2t = -30
5t - 12M = 115
Solving by substitution
Solve either equation for one variable. For example,
7M - 2t = -30 ⇒ t = (7M + 30)/2
Substitute this into the other equation and solve for M.
5 × (7M + 30)/2 - 12M = 115
5 (7M + 30) - 24M = 230
35M + 150 - 24M = 230
11M = 80
M = 80/11
Now solve for t.
t = (7 × (80/11) + 30)/2
t = (560/11 + 30)/2
t = (890/11)/2
t = 445/11
Solving by elimination
Multiply both equations by an appropriate factor to make the coefficients of one of the variables sum to zero. For example,
7M - 2t = -30 ⇒ -10t + 35M = -150 … (multiply by 5)
5t - 12M = 115 ⇒ 10t - 24M = 230 … (multiply by 2)
Now combining the equations eliminates the t terms, and
(-10t + 35M) + (10t - 24M) = -150 + 230
11M = 80
M = 80/11
It follows that
7 × (80/11) - 2t = -30
560/11 - 2t = -30
2t = 890/11
t = 445/11
Just an easy question for 100 Points!
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#1
y=x+5
Shifted 5units left#2
y=3/8
Horizontally Streched by a factor 8/3 parallel to x axis#3
y=-x-2Reflection by y axis as x will be negative and shifting 2 units right
#4
y=6x+1
vertically streched by a factor 6 and shifting 1 units left#5
y=x-11
Shifting 11 units left#6
y=8x
Horizontally streched by 1/8 factor
Answer:
1. Translated 5 units left.
2. Vertical stretch by a factor of 3/8.
3. Reflection in the x-axis, then translated 2 units down.
4. Vertical stretch by a factor of 6, then translated 1 unit up.
5. Translated 11 units down.
6. Vertical stretch by a factor of 8.
7. Vertical stretch by a factor of 1/3, then reflection in the x-axis.
Step-by-step explanation:
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}.[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]
Parent function:
[tex]y=x[/tex]
[tex]\textsf{1.} \quad y=x+5[/tex]
Translated 5 units left.
[tex]\textsf{2.} \quad y=\dfrac{3}{8}x[/tex]
Vertical stretch by a factor of 3/8.
[tex]\textsf{3.} \quad y=-x-2[/tex]
Reflection in the x-axis, then translated 2 units down.
[tex]\textsf{4.} \quad y=6x+1[/tex]
Vertical stretch by a factor of 6, then translated 1 unit up.
[tex]\textsf{5.} \quad y=x-11[/tex]
Translated 11 units down.
[tex]\textsf{6.} \quad y=8x[/tex]
Vertical stretch by a factor of 8.
[tex]\textsf{7.} \quad y=-\dfrac{1}{3}x[/tex]
Vertical stretch by a factor of 1/3, then a reflection in the x-axis.
Which value of a in the exponential function below would cause the function to shrink? f(x) = a(three-halves) superscript x
The value of a in the exponential function is 4/5.
Given the exponential function is f(x)=a(3/2)ˣ.
An function may be a mathematical relation of the subsequent form: f(x)=aˣ. where x may be a variable, and a could be a constant called the exponential of the function.
When multiplying the any function by a constant, we may expand or shrink the function in the y-direction.
y=a(b)ˣ
If a>1 then the function will enlarge.
If a<1 then the function will shrink.
When a=4/5
Then 4/5<1 means the function would shrink.
When a=5/4
Then 5/4>1 means the function would enlarge.
When a=3/2
Then 3/2>1 means the function would enlarge.
When a=7/4
Then 7/4>1 means the function would enlarge.
Hence, the given function f(x)=a(3/2)ˣ would shrink when a=4/5.
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Answer:
4/5
Step-by-step explanation:
got it right
A box is to be constructed with a rectangular base and a height of h cm. the length, l, of the box is 10 cm, and the width, w, is twice the height. which quadratic equation best models the volume of the box? v = lwh
Answer:Answer: We know it has a length of 10 cm, and the width is h times 2.
Step-by-step explanation: So the equation we should write is volume = 10 x (h x 2) x h.
Step-by-step explanation: